2.4.2 first order ode chini

Table 2.1053: first order ode chini [12]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

1594

\begin{align*} y^{\prime }&=-2 x \left (y^{3}-3 y+2\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}

[_separable]

5.102

4703

\begin{align*} y^{\prime }&=a \,x^{\frac {n}{1-n}}+b y^{n} \\ \end{align*}

[[_homogeneous, ‘class G‘], _Chini]

9.194

7143

\begin{align*} -a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Abel]

6.386

11340

\begin{align*} -a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Abel]

8.134

11353

\begin{align*} y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _Chini]

4.525

11354

\begin{align*} y^{\prime }-f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n} \left (a g \left (x \right )+b \right )^{-n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-g^{\prime }\left (x \right ) f \left (x \right )&=0 \\ \end{align*}

[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

2.823

11355

\begin{align*} y^{\prime }-a^{n} f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-g^{\prime }\left (x \right ) f \left (x \right )&=0 \\ \end{align*}

[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

1.281

11487

\begin{align*} x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _Abel]

7.401

11488

\begin{align*} x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

5.869

13637

\begin{align*} y^{\prime }&=a y^{3}+\frac {b}{x^{{3}/{2}}} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Abel]

8.364

13645

\begin{align*} y^{\prime }&=a \,x^{2 n +1} y^{3}+b \,x^{-n -2} \\ \end{align*}

[[_homogeneous, ‘class G‘], _Abel]

10.998

13658

\begin{align*} y^{\prime }&=-\frac {{\mathrm e}^{2 \lambda x} y^{3}}{3 \lambda }+\frac {2 \lambda ^{2} {\mathrm e}^{-\lambda x}}{3} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Abel]

5.053